Trigonometric Graphs & Transformations 1

Which of the following shows the graph of  $y=\sin\ 2x$  ?

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Which of the following shows the graph of  $y=\tan\ \left(x+45\right)\degree$  ?

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Which of the following shows the graph of  $y=2\cos\left(3x\right)-4$  ?

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What is the equation of this graph?

• $y=\sin\left(-2x\right)$

• $y=\cos\left(-x\right)$

• $y=-\cos2x$

• $y=-\sin x$

What is the equation of this graph?

• $y=\tan2x$

• $y=\frac{1}{2}\tan x$

• $y=-\tan\ x$

• $y=\tan\ \frac{1}{2}x$

What is the equation of this graph?

• $y=2\cos3x$

• $y=3\sin2x-1$

• $y=2\sin x-2$

• $y=3\cos x+1$

Describe the transformation from  $y=2\sin x$   to  $y=2\sin x+1$  .

• Graph is shifted downwards by 1 unit.

• Graph is stretched by a factor of 2, parallel to the y-axis, and shifted upwards by 1 unit. 

• Graph is shifted upwards by 1 unit.

• Graph is stretched by a factor of 2, parallel to the y-axis. 

Describe the transformation from  $y=\cos x$  to  $y=3\cos\ \frac{1}{2}x\$  

• Graph is stretched by a factor of 3, parallel to the y-axis and by a factor of  $\frac{1}{4}$ , parallel to the x-axis.

• Graph is stretched by a factor of  $3$  , parallel to the y-axis and by a factor of  $\frac{1}{2}$  , parallel to the x-axis.

• Graph is stretched by a factor of 3, parallel to the y-axis and by a factor of 2 parallel to the x-axis.

• Graph is stretched by a factor of  $\frac{1}{2}$  , parallel to the y-axis and by a factor of 3, parallel to the x-axis. 

Describe the transformation of  $y=\tan\left(x+45\right)\degree$  to  $y=\tan\left(x-45\right)\degree$  .

• Graph is reflected in the x-axis. 

• Graph is shifted to the left by  $90\degree$  

• Graph is shifted to the left by  $45\degree$  

• Graph is shifted to the right by  $90\degree$